Cutting Insert for High Feed Face Milling

ABSTRACT

A cutting insert for milling operations, such as, face milling, slot milling, plunge milling, and ramping operations. The cutting insert exhibits a combination of favorable cutting edge strength, and unique cutting edge geometry, allowing milling operations at relatively high feed rates. The cutting insert includes at least four cutting edges, wherein at least one of the cutting edges is a convex cutting edge.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. §120 as a continuationof co-pending U.S. patent application Ser. No. 13/167,780, filed Jun.24, 2011; which claims priority under §120 as a continuation of U.S.patent application Ser. No. 12/841,206, filed Jul. 22, 2010, whichissued as U.S. Pat. No. 7,988,387 on Aug. 2, 2011; which claims priorityunder §120 as a continuation of U.S. patent application Ser. No.12/340,834, filed Dec. 22, 2008, which issued as U.S. Pat. No. 7,806,634on Oct. 5, 2010; which claims priority under §120 as a continuation ofU.S. patent application Ser. No. 11/696,931, filed Apr. 5, 2007, whichissued as U.S. Pat. No. 7,600,952 on Oct. 13, 2009; which claimspriority under §120 as a continuation of U.S. patent application Ser.No. 10/686,308, filed Oct. 15, 2003, which issued as U.S. Pat. No.7,220,083 on May 22, 2007.

FIELD OF THE INVENTION

The present disclosure is directed to a cutting insert. The cuttinginsert exhibits a combination of favorable cutting edge strength, andunique cutting edge geometry, thus, allowing milling operations atrelatively high feed rates and may be useful in face milling, slotmilling, plunge milling, and ramping operations.

DESCRIPTION OF THE INVENTION BACKGROUND

Traditional machining methods, which are the principal means of removingmetal from workpieces, include chip cutting (such as milling, drilling,turning, broaching, reaming, and tapping) and abrasive machining methods(such as sanding, grinding, and polishing. One such chip cuttingprocess, face milling, may be useful to produce a generally flat surfaceon a workpiece. A face milling tool or “face mill” is so named becausethe flat workpiece surface is produced by action of the face of thetool, although the outside diameter or bevel cutting edge removes mostof the stock. In a typical application, a milling cutter tool comprisinga number of cutting inserts may be driven by a spindle on an axispositioned perpendicular to the surface being milled. ASM Handbook,Volume 16, “Machining” (ASM Intern. 1989) p. 311.

A milling cutter tool produces chips with variable chip thickness. Chipthickness may be used in calculating the maximum load per unit lengthexerted on the edges of a milling cutting tool. An average chipthickness is typically used in such calculations. Average chip thicknesscan be calculated and varies with cutting insert lead angle for the samematerial feed rate. For the example of a substantially square-shapedinsert having four identical cutting edges, a larger lead angle producesa larger average chip thickness during machining, while a smaller leadangle produces chips of smaller average thickness. An example of thevariation of average chip thickness with lead angle of the insert isshown in FIG. 1. FIG. 1 illustrates a comparison of an identicalsquare-shaped insert machining with lead of angles of 90°, 75°, and 45°.As indicated in the FIG. 1, as the lead angle increases from 45° inFIGS. 1( a), to 75° in FIGS. 1( b), to 90° in FIG. 1( c), the averagechip thickness (h_(m)) increases from 0.71 times the feed per tooth ofthe holder (“f_(z)”), to 0.97×(f_(z)), to f_(z). More generally, thechip thickness for a square-shaped cutting insert, or any other inserthaving a linear cutting edge used in a milling cutter tool, may becalculated using the equation h_(m)=f_(z)×sin(K), where h_(m) is theaverage chip thickness, and K is the lead angle measured in the mannershown in FIG. 1.

FIG. 1 also indicates that the length of engaged cutting edge when usinga 90° lead angle is shortest among those scenarios shown in FIG. 1,while the length of engaged cutting edge is longest when the lead angleis 45°. This means that face milling using a 90° lead angle producesmore load, i.e., higher stresses, on the cutting edge per unit lengthcompared with milling using a 45° lead angle, for the same depth of cut.An advantage of reducing load on the cutting edge per unit length isthat reduced load allows for employing a higher feed rate per tooth inthe milling operation and improved tool life. Thus, to reduce theaverage load stresses on the engaged cutting edge, it is clearly anadvantage to use a smaller lead angle.

Square-shaped cutting inserts are commonly used in face and plungemilling because they are strong, indexable and have multiple cuttingedges. Inserts having a substantially square shape or otherwiseincluding four cutting edges are disclosed in, for example, U.S. Pat.Nos. 5,951,212 and 5,454,670, U.S. Published Application No.US2002/0098049, Japanese reference No. 08174327, and PCT Publication No.WO96/35538. A common feature of the inserts disclosed in thesereferences is the combination of four straight cutting edges and eithera planar or a bevel planar clearance (or relief) surface below eachcutting edge.

It is well-known that round-shape inserts, however, have the strongestcutting edge. In addition, round-shaped inserts provide a favorablecombination of maximal corner strength, good material removal capacity,mechanical shock resistance, and thermal distribution. As such,round-shaped face milling inserts are often used for the more demandingmachining applications, such as those involving difficult-to-cutmaterials, hard materials, heat resistant materials, titanium, etc. Inface milling using a round-shaped cutting insert, the lead angle and theextent of the engaged cutting edge will vary with the depth of cut, asshown in FIG. 2. The average chip thickness produced by a round-shapeinsert can be approximately calculated by the following equation (I):

$\begin{matrix}{h_{m} = {\frac{f_{z}}{R} \cdot \sqrt{R^{2} - \left( {R - {doc}} \right)^{2}}}} & (I)\end{matrix}$

where h_(m) is the average chip thickness, f_(z) is the feed per toothfrom a milling cutter, R is the radius of the round-shape cuttinginsert, and doc is the depth of cut. The above equation indicates thatwhen cutting with a round-shaped insert, chip thickness varies withdepth of cut. In contrast, when cutting using a square-shaped insert orany insert having a linear cutting edge, chip thickness does not changewith changes in the depth of cut if the lead angle remains the same (seeFIG. 1).

Furthermore, for the same depth of cut, a larger radius of around-shaped insert always corresponds to a larger portion of thecutting edge engaging the work piece, as illustrated in FIG. 3, thus,reducing the average stress load per unit length on the cutting edge.This, in turn, allows the use of higher feed rates during face millingwithout a loss of quality. However, a limitation of a round-shapedcutting insert lies in that the larger the radius, the larger theinsert. It is difficult to fully utilize the advantages provided byround-shaped inserts of increasingly larger radius in conventionalmachining applications due to their size.

Accordingly, to overcome the cutting edge load problems that may beencountered in face milling with large lead angles, there is a need foran improved design of cutting insert that allows for significantlyincreased feed rates during face milling operations while maintainingthe same or longer tool life of the cutting inserts. Also, there is aneed for a new cutting insert that is similar to a round-shaped insertin that it exhibits favorable cutting edge strength, but also is similarto a square-shaped insert in that it includes multiple cutting edges, isindexable, and also allows for a high feed rate and favorable wearproperties.

SUMMARY

In order to address the foregoing needs, the present disclosure providesa cutting insert for milling operations, such as, face milling, slotmilling, plunge milling, and ramping operations. The cutting insertexhibits a combination of favorable cutting edge strength, and uniquecutting edge geometry, thus, allowing milling operations at relativelyhigh feed rates. The cutting insert includes at least four convexcutting edges. Certain embodiments of square cutting inserts will havefour convex cutting edges which may be connected by nose corners. Theconvex cutting edge may comprise at least one of a circular arc, aportion of an ellipse, a portion of a parabola, a multi-segment splinecurve, a straight line, or combinations of these. Wherein the convexcutting edge comprises a circular arc, the circular arc may have aradius greater than or equal to two times a radius of the largest circlethat may be inscribed on the top surface.

Embodiments of the cutting insert according to the present disclosuremay be produced in the form of, for example, face milling inserts.Relative to conventional cutting inserts having linear cutting edges,embodiments of the cutting inserts according to the present inventionmay allow significantly increased feed rates, reduced radial cuttingforces, increase rates of material removal and increased cutting insertlife. Embodiments of the cutting insert may be robustly designed for usein other milling operations, such as ramping, plunging, and slotting. Inaddition, certain embodiments of a cutter body, disclosed herein, aredesigned to include insert pockets that will accept various cuttinginserts with convex cutting edges.

These and other advantages will be apparent upon consideration of thefollowing description of certain embodiments.

BRIEF DESCRIPTION OF THE FIGURES

Embodiments of the present invention will be understood by reference tothe following figures, wherein:

FIGS. 1( a), 1(b), and 1(c) illustrate variations in the average chipthickness for lead angles of 45°, 75°, and 90° of a substantiallysquare-shaped cutting insert with a linear cutting edge in a typicalmilling operation, wherein the lead angle is measured from the directionof travel of the insert to the cutting edge of the insert;

FIG. 2 illustrates variation in average lead angle for different depthsof cut for application of a substantially round-shaped cutting insert ina typical milling operation;

FIG. 3 illustrates the difference in the extent of engaged cutting edgebetween a substantially round-shaped cutting insert with an 80 mmdiameter and a substantially round-shaped cutting insert with a 20 mmdiameter for a milling operation with a 5 mm depth of cut;

FIGS. 4( a)-(c) illustrate different views of an embodiment of a cuttinginsert with convex cutting edges according to the present disclosure;

FIGS. 5( a)-(d) illustrate several possible convex cutting edge designsof cutting inserts according to the present disclosure;

FIG. 6( a)-(d) depicts steps in the method of the present invention toprepare an embodiment of the cutting tool of the present inventioncomprising at least four convex cutting edges;

FIG. 7 is a perspective view of a milling cutter tool comprising acutter body holding a plurality of cutting inserts;

FIG. 8 includes an enlargement of one pocket of a cutter body comprisinga cutting insert and depicts the relationship between the cutting edgeof an embodiment of the cutting insert of the present invention and theaxis of the cutter body and also depicts the linear movement of thecutting insert relative to the workpiece for face milling, plungemilling, slot milling, and ramping;

FIGS. 9( a) is a top plan views and side views of an embodiment of thecutting insert of the present invention comprising a convex cutting edgepartially defined by a circular arc with a radius of 22.5 mm and FIGS.9( b) is a top plan views and side views of an embodiment of the cuttinginsert of the present invention comprising a convex cutting edgepartially defined by a circular arc with a radius of 55 mm; and

FIG. 10 is a top and side view of another embodiment of the cuttinginsert of the present invention comprising a chip breaking geometry onthe top surface.

DESCRIPTION OF EMBODIMENTS

It is to be understood that certain descriptions of the presentinvention herein have been simplified to illustrate only those elementsand limitations that are relevant to a clear understanding of thepresent invention, while eliminating, for purposes of clarity, otherelements. Those of ordinary skill in the art, upon considering thepresent description of the invention, will recognize that other elementsand/or limitations may be desirable in order to implement the presentinvention. However, because such other elements and/or limitations maybe readily ascertained by one of ordinary skill upon considering thepresent description of the invention, and are not necessary for acomplete understanding of the present invention, a discussion of suchelements and limitations is not provided herein. For example, asdiscussed herein, embodiments of the cutting inserts of the presentdisclosure may be produced in the form of face milling inserts and otherinserts for materials cutting. The manners in which cutting inserts aremanufactured is generally understood by those of ordinary skill in theart and, accordingly, are not described in detail herein. In addition,all the geometric shapes should be considered to be modified by the term“substantially” wherein the term “substantially” means that the shape isformed within typical design and manufacturing tolerances for cuttinginserts.

Furthermore, certain embodiments of the invention according to thepresent disclosure are disclosed in the form of face milling cuttinginserts. It will be understood, however, that the present invention maybe embodied in forms and applied to end uses that are not specificallyand expressly described herein. For example, one skilled in the art willappreciate that embodiments of the present invention may be manufacturedas cutting inserts for other methods of removing metal from work pieces.

Certain embodiments of the present invention are directed to cuttinginserts providing a combination of advantages exhibited by round-shapedcutting inserts having a very large radius, and square-shaped inserts ofconventional size adapted for conventional use in a variety of machiningapplications. Certain other embodiments of the present invention aredirected to a milling cutting tool including embodiments of uniquecutting inserts of the present invention.

These features are provided by an embodiment of the present invention ofa cutting insert having a relatively large cutting edge defined by acurvature radius arc. The cutting insert maintains the overall size ofthe insert as measured by the diameter of an inscribed circle.Additionally, embodiments of the present invention may comprise cuttinginserts with the general shape of any standard cutting insert havingfour or more sides, such as a square, rhombus, or other cutting insertshapes. In the simplest form the convex cutting edge is in the form ofan arc of a circle having a relatively large radius when compared to theradius of a circle inscribed in the top face of the insert. The arc of acircle is considered to be relatively large if the radius of the arc isgreater than or equal to two times the radius of the largest circle thatmay be inscribed in the top surface of the cutting insert. In certainembodiments, the radius of the arc may be greater than or equal to 5times the radius of the largest circle that may be inscribed in the topsurface of the cutting insert, for certain other applications, resultsmay be improved if radius of the arc is greater than or equal to 10times the radius of the largest circle that may be inscribed in the topsurface of the cutting insert. The convex cutting edge has beendescribed initially as comprising a circular arc, however, the convexcutting edge may also comprise portions of an ellipse, portions of aparabola, multi-segment line curves, straight lines, and combinations ofthese.

As a result, embodiments of the cutting insert of the present inventionmay have a convex cutting edge, such as a relatively large curvatureradius on a curved cutting edge, and generate a relatively smooth cutand relatively thin chips. A cutting insert having a convex cutting edgeallows a greater length of engagement for the cutting edge than asimilar conventional cutting insert with a linear cutting edge for thesame depth of cut. This reduces the stress per unit length of thecutting edge and may, in turn, enable the use of relatively high feedrates or longer insert life in comparison with conventional cuttinginserts employed in face milling operations. The convex cutting edge maybe formed on one or more cutting edges of the cutting insert.Preferably, all the cutting surfaces have convex edges so that the toolis fully indexable.

Another advantage provided by certain embodiments of the cutting insertof the present invention draws on features of a square-shaped insert,which typically are relatively robustly designed such that the samecutting insert can be used for plunge, slot, and ramping millingapplications, in addition to high feed face milling applications. Also,a cutter body according to certain embodiments of the present inventionmay be designed such that the same insert pocket can receive cuttinginserts of different convex cutting edges. Accordingly, embodiments ofthe cutting insert of the present disclosure perform in a fashionsimilar to round-shaped cutting insert having a relatively large radiusbut are much more versatile.

Embodiments of the present invention include a generally square-shapedcutting insert with four convex cutting edges. The four cutting edgesmay or may not be identical. In addition, each of the convex cuttingedges may include several regions. For example, a first region mayinclude a curved cutting edge portion having a relatively largecurvature radius. One or more other regions of each convex cutting edgeinclude a substantially straight or linear cutting edge as viewed from atop portion of the cutting insert. The first region of the convexcutting edge portion of the cutting insert may form a generally conicalclearance (or relief) surface on a side surface of the cutting insert.Based on combining features of a relatively large round-shaped insertand a square-shaped insert of conventional size, a method has beendeveloped, discussed below, that may be used to guide the design of thecutting edges of certain embodiments of the cutting insert of thepresent invention.

Certain machining applications require a relatively positive cuttingaction. Therefore, a chip breaker feature may also optionally beincluded in embodiments of the cutting inserts of the presentdisclosure. A chip breaker is typically a built-in feature at the topportion of a milling cutting insert. A chip breaker often ischaracterized by certain basic parameters, such as groove depth, rakeangle, backwall land and groove width, to provide positive cuttingactions with lower cutting power in face milling operations.

An embodiment of the cutting insert, referenced as 10, is shown in FIG.4. The cutting insert 10 may be made of any of the various materialsadapted for cutting applications. Such materials include wear resistantmaterials, such as steel, metal carbides, composites, such as aluminumoxide and metal carbides, tungsten carbides, ceramics, cermets as wellas other materials known in the art. The material may additionally becoated to improve the properties of the cutting insert in certainapplications. As shown in FIG. 4( a), an embodiment of the cuttinginsert 10 defines a central bore 13, a top face 15, a bottom face 17,and four identical cutting edges 12 formed around the periphery of thetop face 15. FIG. 4( b) is a top view of the cutting insert 10, lookingdown at top surface 15, and with bottom edge 21 and the several edgesformed on each side surface 19 indicated in broken lines. FIG. 4( c) isa side elevational view of cutting insert 10 in the direction of arrowsA-A in FIG. 4( a). As best shown in FIGS. 4( a) and 4(c), each sidesurface 19 of the insert 10 includes several clearance surfaces formedbetween the cutting edge 12 and the bottom edge 21, formed around theperiphery of the bottom face 17. In this embodiment, each of the fourconvex cutting edges 12 consists of several regions, including a curvedcutting edge region 25 with a large curvature radius, and twosubstantially straight (i.e., linear) cutting edge regions 27 and 29.The four convex cutting edges 12 of cutting insert 10 are connected bynose corners 23.

Although the cutting edges 12 of cutting insert 10 include these severalregions, alternate embodiments of the cutting insert of the presentdisclosure may include four identical cutting edges including only anose radius and a curved cutting edge portion with a large curvatureradius arc, such as cutting edge regions 23 and 25 of cutting insert 10wherein the large curvature radius arc extends from nose corner 23 to anadjacent nose corner 23. Accordingly, such embodiments do not includeone or more substantially straight (i.e., linear) cutting edge regions,as included in cutting insert 10 as regions 27 and 29.

Returning again to cutting insert 10 of FIG. 4, each of region of thecutting edge 12 of cutting insert 10 forms a distinct clearance surfaceon a side surface 19 of the insert 10. Each such clearance surfaceextends downward from the cutting edge 12 of the insert 10 to the bottomedge 21. For example, as best shown in FIGS. 4( a) and (c), conicalclearance surface 26 extends downward from nose radius 23, conicalclearance surface 28 extends downward from curved cutting edge 25,planar clearance surface 31 extends downward from straight cutting edge27, and planar clearance surface 33 extends downward from straightcutting edge 29. Cutting insert 10 also includes secondary planarclearance surface 35, which extends the clearance surfaces 28, 31, and33 to the bottom edge 21 of the insert 10.

According to the embodiment of FIG. 4, a substantially square-shapedcutting insert 10 includes four convex cutting edges 12, and the curvedcutting edge region 25 of the cutting edge 12 has a relatively largecurvature radius as viewed from the top surface 15 of the cutting insert10. This large curvature radius is preferably significantly larger thanthe nominal radius of the insert's inscribed circle. The curved cuttingedge region 25 then forms the conical clearance surface 28 on the sidesurface 19 of the cutting insert 10.

Accordingly, it will be understood that different embodiments of thecutting insert of the present disclosure may include differentcombinations of distinct cutting edge regions. For example, FIG. 5illustrates various designs of the cutting edges of inserts of thepresent disclosure. FIG. 5( a) depicts a substantially square-shapedcutting insert 110 including four identical cutting edges 112, cuttinginsert 110 includes a nose radius region 114 and a convex cutting edgeregion 116. The cutting edges 112 of insert 110 lack linear regions.FIG. 5( b) depicts a substantially square-shaped cutting insert 120including four identical convex cutting edges 122, cutting insert 120includes a nose radius region 124, one substantially linear cutting edgeregion 126, and a curved cutting edge region 128 having a relativelylarge curvature radius. FIG. 5( c) depicts a substantially square-shapedcutting insert 130 including four identical cutting edges 132, cuttinginsert 130 includes a nose radius region 134, two adjacent substantiallylinear cutting edge regions 135 and 136, and a curved cutting edgeregion 138 having a relatively large curvature radius. FIG. 5( d)depicts a substantially square-shaped cutting insert 140 including fouridentical cutting edges 142, cutting insert 140 includes a nose radiusregion 143, three adjacent substantially linear cutting edge regions144, 145, and 146, and a curved cutting edge region 148 having arelatively large curvature radius.

Certain embodiments of cutting inserts according to the presentdisclosure may be generally described mathematically. As an example,reference is made FIG. 6. As known in the art, the diameter of theinscribed circle, A, (i.e., the circle of largest radius fitting withinthe perimeter of the insert surface) generally represents the size of acutting insert. With reference to FIG. 6( a), assume that the origin(i.e., point (0,0)) of Cartesian coordinate system X-Y is at the center,CP, of the inscribed circle A within the cutting insert represented bythe square 210. The equation of the inscribed circle A can be describedbe the following equation (II):

x ² +y ² =R ²   (II)

where R is the radius of inscribed circle A. A unique feature of certainembodiments of cutting inserts according to the present disclosure isthe combination of certain advantages of a relatively large round-shapedinsert and certain advantages of a square-shaped insert of conventionalsize. Each of the four cutting edges 212 of the substantiallysquare-shaped insert will be tangent to the inscribed circle A at theirpoints of contact, P₁, P₂, P₃, and P₄ which can be determined by theabove equation, and can be represented by a group of tangentialequations of the inscribed circle as follows:

P _(ix) X+P _(iy) y=R ²   (III)

where P_(ix) and P_(iy) are X and Y coordinates of the tangent pointsand i=1, . . . , 4. The square insert is set by a lead angle α, which isdirectly related to the maximum depth of cut M to be used when cuttingwith a round-shaped insert. Assume the bottom side of the square 210 inFIG. 6( a) is tangent to the inscribed circle A at the point P₁ (P_(1x),P_(1y)). In that case, P_(1x)=R*(sin α) and P_(1y)=−R*(cos α). Bysubstituting the point (P_(1x), P_(1y)) into the above equation, weobtain the following equation (IV) for the lower side of the square 210in FIG. 6:

(sin α)·x−(cos α)·y=R ²   (IV)

where α is the lead angle.

Equations defining the remaining three sides of the square 210 in FIG. 6may be derived in a similar fashion, resulting in the following set ofequations (V)-(VIII), one representing each side of the square:

$\quad\left\{ \begin{matrix}{{{\left( {\sin \; \alpha} \right) \cdot x} - {\left( {\cos \; \alpha} \right) \cdot y}} = R^{2}} \\{{{\left( {\cos \; \alpha} \right) \cdot x} + {\left( {\sin \; \alpha} \right) \cdot y}} = R^{2}} \\{{{{- \left( {\sin \; \alpha} \right)} \cdot x} + {\left( {\cos \; \alpha} \right) \cdot y}} = R^{2}} \\{{{{- \left( {\cos \; \alpha} \right)} \cdot x} - {\left( {\sin \; \alpha} \right) \cdot y}} = R^{2}}\end{matrix} \right.$

The above group of equations is based on the lead angle that correspondsto the maximal depth of cut. Each of the four cutting edges of theinsert, including the curved cutting edge region having relatively largecurvature radius, will be confined by square 210 formed by equations(V)-(VIII).

Once the above equations (V)-(VIII) have been generated, an arc of anidentical length with a radius greater than inscribed circle A isprovided on each side of square 210, tangent to square 210 at each ofpoints P₁ through P₄. The four identically positioned arcs are shown inFIG. 6( a) as arcs B₁ through B₄. In certain embodiments of the cuttinginsert, a chord of each of the four arcs B₁-B₄ that is parallel to theparticular adjacent side of square 210 defines the curved cutting edgeregion. Thus, with reference to FIG. 6( a), the arc B₁ has radius ofcurvature greater than the radius of inscribed circle A. Dotted line Zis parallel to the side of square 210 tangent to arc B₁ and intersectsarc B₁ at points z′ and z″. The chord C₁ of arc B₁ intermediate pointsz′ and z″ defines the curved cutting edge region 220 of the cuttinginsert. The relatively large radius of curvature of the curved cuttingedge region 220 is indicated by dotted line segments R₁ and R₂, whichextend from curved cutting edge region 220 toward the center point ofthe radius of curvature defining arc B₁. If extended the distance of theradius of curvature of arc B₁, line segments R₁ and R₂ will meet at apoint well beyond center point CP of circle A.

Since in this embodiment, the chord C1 of the arc B1 is parallel to theadjacent side of square 210, the defined curved cutting edge region withlarge curvature radius, has the same lead angle as seen in the abovegroup of equations. In situations where the cutting insert provided inthe present disclosure is to be used primarily for face milling, thetangential line at lower left end point Z¹ of the arc B₁ to beperpendicular to the cutter body axis, such that good surface finish canbe insured on the machined surface that is perpendicular to the cutterbody axis. Then according to the geometric relationship shown in FIG. 6,the length of the chord, C₁, can be represented as a function of themaximal depth of cut and the lead angle a as shown in the followingequation (IX):

L _(b)=doc_(max)/sin α  (IX)

In such case, the curvature radius R_(b) of the curved cutting edgeregion is determined by the following formula:

$\begin{matrix}{R_{b} = {\frac{L_{b}}{2 \cdot {\sin \left( {\theta/2} \right)}} = \frac{L_{b}}{{2 \cdot \sin}\; \alpha}}} & (X)\end{matrix}$

where θ is the arc center angle.

A second step within the design procedure of certain embodiments ofcutting inserts according to the present disclosure may be to add asecond region to the cutting edge, such as in this example, a linearcutting edge region that is perpendicular to the cutting insert axis andtangent to the lower left end point of the arc forming the curvedcutting edge region of the cutting insert. This second step isillustrated by FIG. 6( b), wherein a first linear cutting edge region214 of similar length is added to the end of each curved cutting edgeregion 220. The next step may be to add a second linear cutting edgeregion to the end of the first linear cutting edge region 214 on eachcutting edge. The second linear cutting edge region 216 may be set at arelatively small angle relative to the first linear cutting edge region.This step is illustrated in FIG. 6( c), wherein second linear cuttingedge region 216 is added on each cutting edge to the end of first linearcutting edge region 214. A further additional step may be to add nosecorners to the cutting insert. In this embodiment, the nose corners 218each have an identical radius that smoothly connects and is tangent tothe second linear cutting edge region 216 and the curved cutting edgeregion 220 that each nose corner 218 connects. This step is illustratedin FIG. 6( d), wherein four identical nose corners 218 complete thecutting insert profile 220.

Once the complete convex cutting edge 214, 216, and 220 shown in FIG. 6(d) is defined, all the clearance surfaces (i.e., facets) on the sidesurfaces of the cutting insert may be formed. In the embodiment shown inFIG. 4, the conical clearance (or relief) surface 28 may be formed belowthe curved edge portion 25 having a large curvature radius, thenconnected by a planar clearance face 35 which is extended to the bottomedge 21 of the cutting insert 10. The large curvature radius on eachcurved cutting edge of the above-described insert is much larger thanthe nose radius 23 on each corner of the insert, for example, acurvature radius of 55 mm on the curved cutting edge portion of theconvex cutting edge is compared to the nose radius of 0.8 mm on theinsert corner. The planar facet 33 is formed below the straight edgeportion 29 and the planar facet 31 is formed below the straight edgeportion 27, both on each of four side surfaces of the cutting insert 10.The facet 33 functions as a cutting facet to produce machined surfaceperpendicular to the cutting axis while the facet 31 as an approachangle for plunge milling along the direction of cutting. And finally theconical clearance surface 26 is formed below the nose corner 23.

A plurality of the cutting inserts, such as the embodiment of cuttinginsert 10, may be assembled into a cutting body 41 as shown in FIG. 7and securely positioned into the pocket 42 by a screw 43 through thecenter hole 13 on the cutting insert 10. The cutter may also include aflute 44 that helps evacuate the chips produced during machining.

In certain face milling applications as shown in FIG. 8, the straightcutting edge 29 may be perpendicular to the cutting axis 46 to guaranteegood surface finish on the machined surface. The cutter body 41 isdesigned in a way that the same pocket can receive the cutting inserthaving same size yet different convex cutting edge, and maintain theperpendicular relationship between the straight cutting edge 29 of theinsert 10 and the axis of the cutter 46. FIG. 9 shows an example of thesame size cutting insert having a 12.7 mm in diameter or 6.35 mm inradius of the insert inscribed circle with two different large curvatureradii on the convex cutting edge, i.e., the cutting insert 48 has a 22.5mm radius curve as part of the convex cutting edge, and the cuttinginsert 49 has 55 mm radius curve as part of the convex cutting edge.

The cutter 41 as shown in FIG. 8 may also designed in a way that itallows using the same insert sitting in the same pocket to performmultiple milling functions (facing, slotting, ramping, and plunging) asalready shown in FIG. 8. This means that if the cutting action follows adirection along the machined surface that is perpendicular to the cutteraxis 46, the inserts are performing face or slot milling operations; andif the cutting action follows a direction that is parallel to the cutteraxis 46, the cutting inserts perform a plunge milling operation; andfurther if the cutting action follows a small angle to the surface ofthe work piece to be machined as shown in FIG. 8, the cutting insertsperform a ramping operation.

The cutting inserts provided in this invention are not limited to thecutting insert with a top flat surface but also to the cutting insertswith a chip breaker on the top of the insert surface. Shown in FIG. 10is a design of the cutting insert 61 provided in this invention that hasa chip breaker on the top surface 61. Such a chip breaker can becharacterized by at least five basic parameters like groove depth 62,rake angle 63, backwall 64, and 65 and groove width 66 as well as otherchip breaking features known in the art. The function of the chipbreaker which may be built into embodiments, the cutting inserts of thepresent invention allows the cutting insert and the associated cutter tobe adapted to use in machining a variety of work materials.

It will be understood that the present description illustrates thoseaspects of the invention relevant to a clear understanding of theinvention. Certain aspects of the invention that would be apparent tothose of ordinary skill in the art and that, therefore, would notfacilitate a better understanding of the invention have not beenpresented in order to simplify the present description. Althoughembodiments of the present invention have been described, one ofordinary skill in the art will, upon considering the foregoingdescription, recognize that many modifications and variations of theinvention may be employed. All such variations and modifications of theinvention are intended to be covered by the foregoing description andthe following claims.

1. A milling insert comprising: a top face comprising four identicalconvex cutting edges and four identical nose corners connecting thecutting edges; a bottom face comprising a bottom edge, wherein aperimeter of the top face is greater than a perimeter of the bottomface; four identical side surfaces, each side surface extending betweena cutting edge and the bottom edge, wherein when viewed in elevation,the cutting edge of each side surface includes a straight cutting edgeregion and a curved cutting edge region to the right of the straightcutting edge region; each side surface comprising a first clearancesurface extending from a curved cutting edge region toward the bottomedge, and a first planar surface region extending from the straightcutting edge region toward the bottom edge; and a second clearancesurface extending from each nose corner toward the bottom edge.
 2. Themilling insert of claim 1, wherein the straight cutting edge region isconfigured to produce a machined surface perpendicular to a cutting axisof a milling cutter on which the milling insert is mounted.
 3. Themilling insert of claim 1, wherein each nose corner comprises at leastone of a circular arc, a series of circular arcs, and a multi-segmentspline curve.
 4. The milling insert of claim 1, wherein each firstclearance surface extends from the curved cutting edge region to thebottom edge.
 5. The milling insert of claim 1, wherein a radius of eachcurved cutting edge region is greater than or equal to two times aradius of the largest circle that may be inscribed on the top face. 6.The milling insert of claim 1, wherein a radius of each curved cuttingedge region is greater than or equal to five times a radius of thelargest circle that may be inscribed on the top face.
 7. The millinginsert of claim 1, wherein a radius of each curved cutting edge regionis greater than or equal to ten times a radius of the largest circlethat may be inscribed on the top face.
 8. The milling insert of claim 1,wherein each side surface further comprises a planar clearance surfaceextending from adjacent the curved cutting edge region toward the bottomedge, the planar clearance surface extending the planar surface regiontoward the bottom edge.
 9. The milling insert of claim 1, wherein eachconvex cutting edge further comprises at least one of a portion of anellipse, a portion of a parabola, and a multi-segment spline curve. 10.The cutting insert of claim 1, further comprising chip breaking geometryon the top face.
 11. The cutting insert of claim 1, wherein each convexcutting edge is parallel to the bottom face.
 12. The milling insert ofclaim 1, wherein the milling insert is a face milling insert.
 13. Amethod of machining a material, the method comprising: securing amilling insert to a cutter body including an axis of rotation, themilling insert comprising a top face comprising four identical convexcutting edges and four identical nose corners connecting the cuttingedges, a bottom face comprising a bottom edge, wherein a perimeter ofthe top face is greater than a perimeter of the bottom face, fouridentical side surfaces, each side surface extending between a cuttingedge and the bottom edge, wherein when viewed in elevation, the cuttingedge of each side surface includes a straight cutting edge region and acurved cutting edge region to the right of the straight cutting edgeregion, each side surface comprising a first clearance surface extendingfrom a curved cutting edge region toward the bottom edge, and a firstplanar surface region extending from the straight cutting edge regiontoward the bottom edge, and a second clearance surface extending fromeach nose corner toward the bottom edge, wherein the straight cuttingedge region is substantially perpendicular to the axis of rotation; andmachining the material with the milling insert.
 14. The method of claim13, wherein in the step of machining the material with the millinginsert, the straight cutting edge region provides a machined surface onthe material that is perpendicular to the axis of rotation.
 15. Themethod of claim 14, wherein each nose corner of the milling insertcomprises at least one of a circular arc, a series of circular arcs, anda multi-segment spline curve.
 16. The method of claim 14, wherein eachfirst clearance surface of the milling insert extends from the curvedcutting edge region to the bottom edge.
 17. The method of claim 14,wherein a radius of each curved cutting edge region of the millinginsert is greater than or equal to two times a radius of the largestcircle that may be inscribed on the top face.
 18. The method of claim14, wherein a radius of each curved cutting edge region of the millinginsert is greater than or equal to five times a radius of the largestcircle that may be inscribed on the top face.
 19. The method of claim14, wherein a radius of each curved cutting edge region of the millinginsert is greater than or equal to ten times a radius of the largestcircle that may be inscribed on the top face.
 20. The method of claim14, wherein each side surface of the milling insert further comprises aplanar clearance surface extending from adjacent the curved cutting edgeregion toward the bottom edge, the planar clearance surface extendingthe planar surface region toward the bottom edge.
 21. The method ofclaim 14, wherein each convex cutting edge of the milling insert furthercomprises at least one of a portion of an ellipse, a portion of aparabola, and a multi-segment spline curve.
 22. The method of claim 14,wherein the top face of the milling insert further comprises chipbreaking geometry.
 23. The method of claim 14, wherein each convexcutting edge of the milling insert is parallel to the bottom face. 24.The method of claim 14, wherein the milling insert is a face millinginsert and machining the material comprises face milling the material.